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 Free Download Galois Theory: Fifth Edition by Ian Stewart English | 2023 | ISBN: 1032101598 | 386 pages | True PDF | 36.67 MB  Free Download Lucia Di Vizio , Charlotte Hardouin, "Intrinsic Approach to Galois Theory of Q-difference Equations" English | ISBN: 1470453843 | 2023 | 70 pages | PDF | 1 MB The Galois theory of difference equations has witnessed a major evolution during the past two decades, say Di Vizio and Hardouin, and in the particular case of q-difference equations, several different Galois theories have emerged. They consider here an arithmetic approach to the Galois theory of q-difference equations, and use it to establish an arithmetical description of some of the Galois groups attached to q-difference systems. After an introduction to q-difference equations, they cover the triviality of q-difference equations with rational coefficients, intrinsic Galois groups, and comparison with the non-linear theory.  Free Download Galois Theory and Its Algebraic Background by D.J.H. Garling English | 2022 | ISBN: 1108838928 | 208 pages | True PDF | 7.17 MB Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.  Galois Theory and Modular Forms by Ki-ichiro Hashimoto, Katsuya Miyake, Hiroaki Nakamura English | PDF | 2004 | 392 Pages | ISBN : 1402076894 | 31.1 MB This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts.  Galois Theory by David A. Cox English | PDF | 2004 | 569 Pages | ISBN : 0471434191 | 25.7 MB An introduction to one of the most celebrated theories of mathematics  Automorphic Forms and Galois Representations: Volume 1 By Fred Diamond, Payman L. Kassaei, Minhyong Kim 2014 | 390 Pages | ISBN: 1107691923 | PDF | 3 MB Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.  The Embedding Problem in Galois Theory By Lur'e, Boris B.; Išchanov, Vladimir V.; Faddeev, Dmitrij K 1997 | 182 Pages | ISBN: 0821845926 | DJVU | 2 MB The central problem of modern Galois theory involves the inverse problem: given a field $k$ and a group $G$, construct an extension $L/k$ with Galois group $G$. The embedding problem for fields generalizes the inverse problem and consists in finding the conditions under which one can construct a field $L$ normal over $k$, with group $G$, such that $L$ extends a given normal extension $K/k$ with Galois group $G/A$. Moreover, the requirements applied to the object $L$ to be found are usually weakened: it is not necessary for $L$ to be a field, but $L$ must be a Galois algebra over the field $k$, with group $G$. In this setting the embedding problem is rich in content. But the inverse problem in terms of Galois algebras is poor in content because a Galois algebra providing a solution of the inverse problem always exists and may be easily constructed. The embedding problem is a fruitful approach to the solution of the inverse problem in Galois theory. This book is based on D. K. Faddeev's lectures on embedding theory at St. Petersburg University and contains the main results on the embedding problem. All stages of development are presented in a methodical and unified manner  The Eigenbook: Eigenvarieties, families of Galois representations, p-adic L-functions (Pathways in Mathematics) English | 2021 | ISBN: 3030772624 | 319 Pages | PDF EPUB | 16 MB
 Galois' Dream: Group Theory and Differential Equations: Group Theory and Differential Equations by Michio Kuga English | February 5, 1993 | ISBN: 0817636889 | 159 pages | PDF | 7.22 Mb First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience--an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.  Galois Fields in Quantum Mechanics: Quantum Special General Relativity (QSGR) by Ed Gerck Ph.D. English | April 4, 2020 | ISBN: N/A | ASIN: B086PVSGN2 | 113 pages | PDF | 0.96 Mb The conclusion that the measurement of extremely small distances is physically impossible, which preempts continuity, was already considered by Leon Brillouin ca. 1956, and now is proved in this work, as well as reporting on new results including Galois fields as an exact calculation of physical quantities.As people are trying to understand the limitations of our intuitions about quantum processes, the second derivative is included in the force expression (e.g., Schroedinger equation) and this cannot be "doomed" to be continuous beforehand. If the second derivative exists, one should not have to expect necessarily a continuous field. Can be quantum, it is the hypothesis. Galois fields then work as a model. The scalability of quantum computing and the unification of general relativity with quantum mechanics, follow. |
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